How to Calculate Cross-Price Elasticity of Demand
Cross-price elasticity = %Δ quantity demanded of good A ÷ %Δ price of good B. Positive means substitutes; negative means complements.
Formula
XED = %ΔQd of good A ÷ %ΔP of good B. XED > 0 → substitutes; XED < 0 → complements; XED ≈ 0 → unrelated goods.
Steps
- 1Find the % change in the price of good B. The good whose price changed.
- 2Find the % change in quantity demanded of good A. The other good — the one whose demand responds.
- 3Divide. XED = %ΔQd(A) ÷ %ΔP(B). Keep the sign — it carries the meaning.
- 4Interpret the sign. Positive = substitutes (buyers switch toward A when B gets pricier); negative = complements (goods consumed together).
Worked example
Coffee prices rise 10% and quantity of tea demanded rises 4%: XED = 4% ÷ 10% = +0.4, so coffee and tea are substitutes. If hot dog prices rise 10% and bun purchases fall 5%, XED = −5% ÷ 10% = −0.5 — complements.
Frequently asked questions
What does the size of cross-price elasticity tell you?
The sign identifies the relationship and the magnitude shows its strength: an XED of +2 means much closer substitutes than +0.2.
How is cross-price elasticity different from price elasticity of demand?
PED measures how a good's own quantity responds to its own price; XED measures how one good's quantity responds to a different good's price.
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